Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 17


$$ y=e(x+2).$$

Work Step by Step

We have $$ y'=e^{x+2}\Longrightarrow y'(-1)=e.$$ Then the slope of the tangent line at $ x=-1$ is $ m= e $. Hence the equation of the tangent line is given by $$ y=mx+c=ex+c.$$ Since $ y(-1)=e $, then $ c=2e $, hence the tangent line at $ x=-1$ is given by $$ y=ex+2e=e(x+2).$$
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